Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
Michael R. Douglas, Robert L. Karp, Sergio Lukic, Rene Reinbacher
Abstract
We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.
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